DSolve[Derivative[1][y][x] == -(x*(-513 - 432*x - 1134*x^2 - 756*x^3 - 864*x^4 - 576*x^5 - 456*x^6 - 144*x^7 - 96*x^8 + 64*x^9 - 378*y[x] - 594*x^2*y[x] + 720*x^3*y[x] - 216*x^4*y[x] + 1008*x^5*y[x] - 288*x^6*y[x] + 288*x^7*y[x] - 288*x^8*y[x] - 540*y[x]^2 - 1296*x^2*y[x]^2 + 432*x^3*y[x]^2 - 972*x^4*y[x]^2 + 864*x^5*y[x]^2 - 216*x^6*y[x]^2 + 432*x^7*y[x]^2 - 216*y[x]^3 - 648*x^2*y[x]^3 - 648*x^4*y[x]^3 - 216*x^6*y[x]^3))/(216*(1 + x^2)^4),y[x],x]